There's something to be said about the word "Legendary". In a game about pirates you would think a "Flying Dutchman" or a "Queen Anne's Revenge" would surface. No, you see, in this game, it would be the unearthly talents that each of the five ships possess that make them legendary.
The Legendary Ships that you can unlock by taking over the forts in each of the four corners of the map aren't all that fancy looking, but they will absolutely make sure they give you a Legendary challenge. Once the 4 forts have been taken over, you will then see the large red ships appear on the map, out in the middle of nowhere in each corner.
Before you even consider taking on any of the Legendary Ships, you will need to have your ship upgraded fully. You don't necessarily need the elite upgrades, although I would suggest it for the hull. That elite upgrade can be found in the San Ignacio Wreck. The cannons, heavy shot, chain-shots, mortars, and swivels will all need to be up to the fullest however.
For your troubles, once you defeat all 5 Legendary Ships, you will receive the Devil of the Caribbean achievement/trophy as well as a special charge attack.